KM3NeT’s detection of a muon track produced by a $\sim 220 \, {\rm PeV}$ neutrino provides an opportunity to probe physics at center-of-momentum energies greater than those probed by the Large Hadron Collider or other existing particle accelerators. In this study, we use this single event to place an upper limit on the neutrino-nucleon cross section of $\sigma_{\nu N} < 26 \, \sigma_{\nu N}^{\rm SM}$ at $E_{\rm CM} \sim 20 \, {\rm TeV}$. This result can be used to constrain a variety of scenarios beyond the Standard Model. With future very large volume neutrino telescopes, constraints on the neutrino-nucleon scattering cross section are expected to become substantially more stringent and, in some scenarios, could become competitive with accelerator probes of new physics.